Differential Space–Time Block Coding for Phase-Unsynchronized Cell-Free MIMO Downlink

In the downlink of CF-mMIMO systems, spectral efficiency gains critically rely on joint coherent transmission, as all APs must align their transmitted signals in phase at the UE. Achieving such phase alignment is challenging, as it requires tight synchronization among geographically distributed APs. In this paper, we address this issue by introducing a DSTBC approach that bypasses the need for AP phase synchronization. We first provide analytic bounds to the achievable spectral efficiency of CF-mMIMO with phase-unsynchronized APs. Then, we propose a DSTBC-based transmission scheme tailored to CF-mMIMO, which operates without CSI and phase synchronization among the APs. We derive a closed-form expression for the resulting SINR, enabling quantitative comparisons among different DSTBC schemes. Numerical simulations confirm that phase misalignments can significantly impair system performance. In contrast, the proposed DSTBC scheme can mitigate these effects, achieving performance comparable to that of fully synchronized systems. However, when more than two APs jointly serve a UE, the code rate of DSTBC schemes can limit their SE gains. Hence, we also investigate DQO-STBC schemes that achieve full code rate by relaxing the orthogonality constraints.